Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.151613669376.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(2.56149 - 0.662382i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.451 |
Dual form | 1050.3.p.c.901.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −0.440173 | − | 6.98615i | −0.0628819 | − | 0.998021i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.76860 | + | 6.52741i | −0.342600 | + | 0.593401i | −0.984915 | − | 0.173040i | \(-0.944641\pi\) |
0.642315 | + | 0.766441i | \(0.277974\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.250000 | − | 0.144338i | ||||
\(13\) | − | 21.3906i | − | 1.64543i | −0.568451 | − | 0.822717i | \(-0.692457\pi\) | ||
0.568451 | − | 0.822717i | \(-0.307543\pi\) | |||||||
\(14\) | −8.24500 | + | 5.47905i | −0.588928 | + | 0.391361i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 18.1757 | + | 10.4937i | 1.06916 | + | 0.617278i | 0.927951 | − | 0.372703i | \(-0.121569\pi\) |
0.141205 | + | 0.989980i | \(0.454902\pi\) | |||||||
\(18\) | 2.12132 | − | 3.67423i | 0.117851 | − | 0.204124i | ||||
\(19\) | 20.8728 | − | 12.0509i | 1.09857 | − | 0.634260i | 0.162726 | − | 0.986671i | \(-0.447971\pi\) |
0.935845 | + | 0.352411i | \(0.114638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.38992 | + | 10.8604i | −0.256663 | + | 0.517163i | ||||
\(22\) | 10.6592 | 0.484510 | ||||||||
\(23\) | 2.79005 | + | 4.83250i | 0.121306 | + | 0.210109i | 0.920283 | − | 0.391253i | \(-0.127958\pi\) |
−0.798977 | + | 0.601362i | \(0.794625\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −26.1981 | + | 15.1255i | −1.00762 | + | 0.581749i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 12.5405 | + | 6.22374i | 0.447876 | + | 0.222277i | ||||
\(29\) | −9.96625 | −0.343664 | −0.171832 | − | 0.985126i | \(-0.554969\pi\) | ||||
−0.171832 | + | 0.985126i | \(0.554969\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.70073 | + | 3.29132i | 0.183894 | + | 0.106171i | 0.589121 | − | 0.808045i | \(-0.299474\pi\) |
−0.405227 | + | 0.914216i | \(0.632807\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 11.3058 | − | 6.52741i | 0.342600 | − | 0.197800i | ||||
\(34\) | − | 29.6807i | − | 0.872962i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 11.1983 | + | 19.3960i | 0.302656 | + | 0.524216i | 0.976737 | − | 0.214442i | \(-0.0687933\pi\) |
−0.674080 | + | 0.738658i | \(0.735460\pi\) | |||||||
\(38\) | −29.5187 | − | 17.0426i | −0.776807 | − | 0.448490i | ||||
\(39\) | −18.5248 | + | 32.0860i | −0.474996 | + | 0.822717i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 51.0827i | − | 1.24592i | −0.782254 | − | 0.622959i | \(-0.785930\pi\) | ||
0.782254 | − | 0.622959i | \(-0.214070\pi\) | |||||||
\(42\) | 17.1125 | − | 1.07820i | 0.407440 | − | 0.0256714i | ||||
\(43\) | −34.7656 | −0.808503 | −0.404252 | − | 0.914648i | \(-0.632468\pi\) | ||||
−0.404252 | + | 0.914648i | \(0.632468\pi\) | |||||||
\(44\) | −7.53720 | − | 13.0548i | −0.171300 | − | 0.296700i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.94572 | − | 6.83419i | 0.0857766 | − | 0.148569i | ||||
\(47\) | 67.2462 | − | 38.8246i | 1.43077 | − | 0.826056i | 0.433591 | − | 0.901110i | \(-0.357246\pi\) |
0.997179 | + | 0.0750536i | \(0.0239128\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −48.6125 | + | 6.15023i | −0.992092 | + | 0.125515i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.1757 | − | 31.4812i | −0.356385 | − | 0.617278i | ||||
\(52\) | 37.0497 | + | 21.3906i | 0.712494 | + | 0.411359i | ||||
\(53\) | 24.8989 | − | 43.1262i | 0.469791 | − | 0.813703i | −0.529612 | − | 0.848240i | \(-0.677662\pi\) |
0.999403 | + | 0.0345374i | \(0.0109958\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.24500 | − | 19.7598i | −0.0222321 | − | 0.352854i | ||||
\(57\) | −41.7457 | −0.732381 | ||||||||
\(58\) | 7.04720 | + | 12.2061i | 0.121504 | + | 0.210450i | ||||
\(59\) | 72.9362 | + | 42.1098i | 1.23621 | + | 0.713725i | 0.968317 | − | 0.249725i | \(-0.0803401\pi\) |
0.267890 | + | 0.963449i | \(0.413673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.4404 | + | 41.8235i | −1.18755 | + | 0.685631i | −0.957749 | − | 0.287607i | \(-0.907140\pi\) |
−0.229799 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(62\) | − | 9.30925i | − | 0.150149i | ||||||
\(63\) | 17.4903 | − | 11.6228i | 0.277624 | − | 0.184489i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −15.9888 | − | 9.23115i | −0.242255 | − | 0.139866i | ||||
\(67\) | 33.2911 | − | 57.6618i | 0.496882 | − | 0.860625i | −0.503112 | − | 0.864221i | \(-0.667812\pi\) |
0.999994 | + | 0.00359682i | \(0.00114491\pi\) | |||||||
\(68\) | −36.3513 | + | 20.9874i | −0.534578 | + | 0.308639i | ||||
\(69\) | − | 9.66501i | − | 0.140073i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −68.1049 | −0.959224 | −0.479612 | − | 0.877481i | \(-0.659223\pi\) | ||||
−0.479612 | + | 0.877481i | \(0.659223\pi\) | |||||||
\(72\) | 4.24264 | + | 7.34847i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −75.9128 | − | 43.8283i | −1.03990 | − | 0.600387i | −0.120096 | − | 0.992762i | \(-0.538320\pi\) |
−0.919805 | + | 0.392375i | \(0.871654\pi\) | |||||||
\(74\) | 15.8368 | − | 27.4301i | 0.214010 | − | 0.370677i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.2038i | 0.634260i | ||||||||
\(77\) | 47.2603 | + | 23.4548i | 0.613770 | + | 0.304608i | ||||
\(78\) | 52.3962 | 0.671746 | ||||||||
\(79\) | −49.3730 | − | 85.5165i | −0.624974 | − | 1.08249i | −0.988546 | − | 0.150921i | \(-0.951776\pi\) |
0.363572 | − | 0.931566i | \(-0.381557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −62.5632 | + | 36.1209i | −0.762966 | + | 0.440499i | ||||
\(83\) | − | 26.9448i | − | 0.324636i | −0.986739 | − | 0.162318i | \(-0.948103\pi\) | ||
0.986739 | − | 0.162318i | \(-0.0518970\pi\) | |||||||
\(84\) | −13.4209 | − | 20.1960i | −0.159772 | − | 0.240429i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.5830 | + | 42.5790i | 0.285849 | + | 0.495105i | ||||
\(87\) | 14.9494 | + | 8.63103i | 0.171832 | + | 0.0992072i | ||||
\(88\) | −10.6592 | + | 18.4623i | −0.121127 | + | 0.209799i | ||||
\(89\) | 12.0453 | − | 6.95436i | 0.135341 | − | 0.0781389i | −0.430801 | − | 0.902447i | \(-0.641769\pi\) |
0.566142 | + | 0.824308i | \(0.308436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −149.438 | + | 9.41559i | −1.64218 | + | 0.103468i | ||||
\(92\) | −11.1602 | −0.121306 | ||||||||
\(93\) | −5.70073 | − | 9.87395i | −0.0612981 | − | 0.106171i | ||||
\(94\) | −95.1005 | − | 54.9063i | −1.01171 | − | 0.584110i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | − | 3.69132i | − | 0.0380549i | −0.999819 | − | 0.0190274i | \(-0.993943\pi\) | ||
0.999819 | − | 0.0190274i | \(-0.00605698\pi\) | |||||||
\(98\) | 41.9067 | + | 55.1890i | 0.427619 | + | 0.563153i | ||||
\(99\) | −22.6116 | −0.228400 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −158.170 | − | 91.3195i | −1.56604 | − | 0.904154i | −0.996624 | − | 0.0821041i | \(-0.973836\pi\) |
−0.569416 | − | 0.822049i | \(-0.692831\pi\) | |||||||
\(102\) | −25.7043 | + | 44.5211i | −0.252003 | + | 0.436481i | ||||
\(103\) | −78.8521 | + | 45.5253i | −0.765555 | + | 0.441993i | −0.831287 | − | 0.555844i | \(-0.812395\pi\) |
0.0657318 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(104\) | − | 60.5019i | − | 0.581749i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −70.4249 | −0.664385 | ||||||||
\(107\) | −25.7682 | − | 44.6318i | −0.240824 | − | 0.417120i | 0.720125 | − | 0.693844i | \(-0.244084\pi\) |
−0.960949 | + | 0.276724i | \(0.910751\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −19.1807 | + | 33.2219i | −0.175970 | + | 0.304788i | −0.940496 | − | 0.339804i | \(-0.889639\pi\) |
0.764527 | + | 0.644592i | \(0.222973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 38.7920i | − | 0.349477i | ||||||
\(112\) | −23.3204 | + | 15.4971i | −0.208218 | + | 0.138367i | ||||
\(113\) | −198.558 | −1.75715 | −0.878573 | − | 0.477608i | \(-0.841504\pi\) | ||||
−0.878573 | + | 0.477608i | \(0.841504\pi\) | |||||||
\(114\) | 29.5187 | + | 51.1278i | 0.258936 | + | 0.448490i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.96625 | − | 17.2621i | 0.0859160 | − | 0.148811i | ||||
\(117\) | 55.5745 | − | 32.0860i | 0.474996 | − | 0.274239i | ||||
\(118\) | − | 119.104i | − | 1.00936i | ||||||
\(119\) | 65.3102 | − | 131.597i | 0.548825 | − | 1.10586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.0953 | + | 55.5907i | 0.265250 | + | 0.459427i | ||||
\(122\) | 102.446 | + | 59.1474i | 0.839723 | + | 0.484814i | ||||
\(123\) | −44.2389 | + | 76.6240i | −0.359666 | + | 0.622959i | ||||
\(124\) | −11.4015 | + | 6.58263i | −0.0919472 | + | 0.0530857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −26.6025 | − | 13.2026i | −0.211131 | − | 0.104782i | ||||
\(127\) | −74.1132 | −0.583569 | −0.291784 | − | 0.956484i | \(-0.594249\pi\) | ||||
−0.291784 | + | 0.956484i | \(0.594249\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 52.1485 | + | 30.1079i | 0.404252 | + | 0.233395i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3500 | − | 10.0170i | 0.132443 | − | 0.0764657i | −0.432315 | − | 0.901723i | \(-0.642303\pi\) |
0.564757 | + | 0.825257i | \(0.308970\pi\) | |||||||
\(132\) | 26.1096i | 0.197800i | ||||||||
\(133\) | −93.3773 | − | 140.516i | −0.702085 | − | 1.05651i | ||||
\(134\) | −94.1614 | −0.702697 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 51.4085 | + | 29.6807i | 0.378004 | + | 0.218241i | ||||
\(137\) | 43.0853 | − | 74.6259i | 0.314491 | − | 0.544715i | −0.664838 | − | 0.746988i | \(-0.731499\pi\) |
0.979329 | + | 0.202273i | \(0.0648328\pi\) | |||||||
\(138\) | −11.8372 | + | 6.83419i | −0.0857766 | + | 0.0495231i | ||||
\(139\) | 232.502i | 1.67268i | 0.548213 | + | 0.836339i | \(0.315308\pi\) | ||||
−0.548213 | + | 0.836339i | \(0.684692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −134.492 | −0.953847 | ||||||||
\(142\) | 48.1574 | + | 83.4111i | 0.339137 | + | 0.587402i | ||||
\(143\) | 139.625 | + | 80.6128i | 0.976402 | + | 0.563726i | ||||
\(144\) | 6.00000 | − | 10.3923i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 123.965i | 0.849076i | ||||||||
\(147\) | 78.2450 | + | 32.8743i | 0.532279 | + | 0.223635i | ||||
\(148\) | −44.7931 | −0.302656 | ||||||||
\(149\) | 109.963 | + | 190.462i | 0.738008 | + | 1.27827i | 0.953391 | + | 0.301738i | \(0.0975666\pi\) |
−0.215383 | + | 0.976530i | \(0.569100\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130.461 | − | 225.965i | 0.863980 | − | 1.49646i | −0.00407633 | − | 0.999992i | \(-0.501298\pi\) |
0.868056 | − | 0.496466i | \(-0.165369\pi\) | |||||||
\(152\) | 59.0373 | − | 34.0852i | 0.388403 | − | 0.224245i | ||||
\(153\) | 62.9623i | 0.411518i | ||||||||
\(154\) | −4.69190 | − | 74.4668i | −0.0304669 | − | 0.483551i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −37.0497 | − | 64.1719i | −0.237498 | − | 0.411359i | ||||
\(157\) | −98.8921 | − | 57.0954i | −0.629886 | − | 0.363665i | 0.150822 | − | 0.988561i | \(-0.451808\pi\) |
−0.780708 | + | 0.624896i | \(0.785141\pi\) | |||||||
\(158\) | −69.8239 | + | 120.939i | −0.441923 | + | 0.765434i | ||||
\(159\) | −74.6968 | + | 43.1262i | −0.469791 | + | 0.271234i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.5325 | − | 21.6188i | 0.202065 | − | 0.134278i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −24.3581 | − | 42.1894i | −0.149436 | − | 0.258831i | 0.781583 | − | 0.623801i | \(-0.214412\pi\) |
−0.931019 | + | 0.364970i | \(0.881079\pi\) | |||||||
\(164\) | 88.4777 | + | 51.0827i | 0.539498 | + | 0.311480i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.0005 | + | 19.0528i | −0.198798 | + | 0.114776i | ||||
\(167\) | 49.6127i | 0.297082i | 0.988906 | + | 0.148541i | \(0.0474577\pi\) | ||||
−0.988906 | + | 0.148541i | \(0.952542\pi\) | |||||||
\(168\) | −15.2450 | + | 30.7179i | −0.0907440 | + | 0.182845i | ||||
\(169\) | −288.560 | −1.70745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 62.6185 | + | 36.1528i | 0.366190 | + | 0.211420i | ||||
\(172\) | 34.7656 | − | 60.2159i | 0.202126 | − | 0.350092i | ||||
\(173\) | −203.811 | + | 117.670i | −1.17810 | + | 0.680176i | −0.955574 | − | 0.294751i | \(-0.904763\pi\) |
−0.222525 | + | 0.974927i | \(0.571430\pi\) | |||||||
\(174\) | − | 24.4122i | − | 0.140300i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30.1488 | 0.171300 | ||||||||
\(177\) | −72.9362 | − | 126.329i | −0.412069 | − | 0.713725i | ||||
\(178\) | −17.0346 | − | 9.83495i | −0.0957002 | − | 0.0552525i | ||||
\(179\) | 22.1049 | − | 38.2868i | 0.123491 | − | 0.213893i | −0.797651 | − | 0.603119i | \(-0.793924\pi\) |
0.921142 | + | 0.389226i | \(0.127258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 117.049i | 0.646679i | 0.946283 | + | 0.323340i | \(0.104806\pi\) | ||||
−0.946283 | + | 0.323340i | \(0.895194\pi\) | |||||||
\(182\) | 117.200 | + | 176.366i | 0.643958 | + | 0.969043i | ||||
\(183\) | 144.881 | 0.791699 | ||||||||
\(184\) | 7.89145 | + | 13.6684i | 0.0428883 | + | 0.0742847i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.06204 | + | 13.9639i | −0.0433443 | + | 0.0750746i | ||||
\(187\) | −136.994 | + | 79.0933i | −0.732586 | + | 0.422959i | ||||
\(188\) | 155.299i | 0.826056i | ||||||||
\(189\) | −36.3011 | + | 2.28721i | −0.192069 | + | 0.0121016i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −117.156 | − | 202.920i | −0.613383 | − | 1.06241i | −0.990666 | − | 0.136313i | \(-0.956475\pi\) |
0.377283 | − | 0.926098i | \(-0.376858\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 9.78252 | − | 16.9438i | 0.0506866 | − | 0.0877918i | −0.839569 | − | 0.543253i | \(-0.817192\pi\) |
0.890256 | + | 0.455461i | \(0.150526\pi\) | |||||||
\(194\) | −4.52093 | + | 2.61016i | −0.0233037 | + | 0.0134544i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 37.9600 | − | 90.3495i | 0.193673 | − | 0.460967i | ||||
\(197\) | −179.443 | −0.910877 | −0.455438 | − | 0.890267i | \(-0.650517\pi\) | ||||
−0.455438 | + | 0.890267i | \(0.650517\pi\) | |||||||
\(198\) | 15.9888 | + | 27.6934i | 0.0807516 | + | 0.139866i | ||||
\(199\) | −221.630 | − | 127.958i | −1.11372 | − | 0.643006i | −0.173928 | − | 0.984758i | \(-0.555646\pi\) |
−0.939790 | + | 0.341753i | \(0.888979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −99.8732 | + | 57.6618i | −0.496882 | + | 0.286875i | ||||
\(202\) | 258.291i | 1.27867i | ||||||||
\(203\) | 4.38688 | + | 69.6257i | 0.0216102 | + | 0.342984i | ||||
\(204\) | 72.7026 | 0.356385 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 111.514 | + | 64.3825i | 0.541329 | + | 0.312536i | ||||
\(207\) | −8.37014 | + | 14.4975i | −0.0404355 | + | 0.0700363i | ||||
\(208\) | −74.0994 | + | 42.7813i | −0.356247 | + | 0.205679i | ||||
\(209\) | 181.661i | 0.869190i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 196.891 | 0.933132 | 0.466566 | − | 0.884486i | \(-0.345491\pi\) | ||||
0.466566 | + | 0.884486i | \(0.345491\pi\) | |||||||
\(212\) | 49.7979 | + | 86.2525i | 0.234896 | + | 0.406851i | ||||
\(213\) | 102.157 | + | 58.9806i | 0.479612 | + | 0.276904i | ||||
\(214\) | −36.4417 | + | 63.1189i | −0.170288 | + | 0.294948i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 20.4843 | − | 41.2749i | 0.0943977 | − | 0.190207i | ||||
\(218\) | 54.2512 | 0.248859 | ||||||||
\(219\) | 75.9128 | + | 131.485i | 0.346634 | + | 0.600387i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 224.467 | − | 388.789i | 1.01569 | − | 1.75923i | ||||
\(222\) | −47.5103 | + | 27.4301i | −0.214010 | + | 0.123559i | ||||
\(223\) | − | 431.015i | − | 1.93280i | −0.257039 | − | 0.966401i | \(-0.582747\pi\) | ||
0.257039 | − | 0.966401i | \(-0.417253\pi\) | |||||||
\(224\) | 35.4700 | + | 17.6034i | 0.158348 | + | 0.0785866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 140.401 | + | 243.182i | 0.621245 | + | 1.07603i | ||||
\(227\) | 151.637 | + | 87.5479i | 0.668006 | + | 0.385673i | 0.795321 | − | 0.606189i | \(-0.207302\pi\) |
−0.127315 | + | 0.991862i | \(0.540636\pi\) | |||||||
\(228\) | 41.7457 | − | 72.3057i | 0.183095 | − | 0.317130i | ||||
\(229\) | 29.0717 | − | 16.7846i | 0.126951 | − | 0.0732951i | −0.435180 | − | 0.900344i | \(-0.643315\pi\) |
0.562131 | + | 0.827048i | \(0.309982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −50.5779 | − | 76.1108i | −0.218952 | − | 0.329484i | ||||
\(232\) | −28.1888 | −0.121504 | ||||||||
\(233\) | 77.4567 | + | 134.159i | 0.332432 | + | 0.575790i | 0.982988 | − | 0.183669i | \(-0.0587973\pi\) |
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(234\) | −78.5942 | − | 45.3764i | −0.335873 | − | 0.193916i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −145.872 | + | 84.2195i | −0.618104 | + | 0.356862i | ||||
\(237\) | 171.033i | 0.721658i | ||||||||
\(238\) | −207.354 | + | 13.0647i | −0.871235 | + | 0.0548935i | ||||
\(239\) | 316.591 | 1.32465 | 0.662325 | − | 0.749217i | \(-0.269570\pi\) | ||||
0.662325 | + | 0.749217i | \(0.269570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 202.219 | + | 116.751i | 0.839084 | + | 0.484446i | 0.856953 | − | 0.515395i | \(-0.172355\pi\) |
−0.0178685 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(242\) | 45.3896 | − | 78.6171i | 0.187560 | − | 0.324864i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 167.294i | − | 0.685631i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 125.126 | 0.508644 | ||||||||
\(247\) | −257.777 | − | 446.484i | −1.04363 | − | 1.80763i | ||||
\(248\) | 16.1241 | + | 9.30925i | 0.0650165 | + | 0.0375373i | ||||
\(249\) | −23.3349 | + | 40.4172i | −0.0937143 | + | 0.162318i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 56.6879i | − | 0.225848i | −0.993604 | − | 0.112924i | \(-0.963978\pi\) | ||
0.993604 | − | 0.112924i | \(-0.0360217\pi\) | |||||||
\(252\) | 2.64104 | + | 41.9169i | 0.0104803 | + | 0.166337i | ||||
\(253\) | −42.0583 | −0.166238 | ||||||||
\(254\) | 52.4060 | + | 90.7698i | 0.206323 | + | 0.357361i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 251.528 | − | 145.219i | 0.978706 | − | 0.565056i | 0.0768270 | − | 0.997044i | \(-0.475521\pi\) |
0.901879 | + | 0.431988i | \(0.142188\pi\) | |||||||
\(258\) | − | 85.1581i | − | 0.330070i | ||||||
\(259\) | 130.574 | − | 86.7704i | 0.504147 | − | 0.335021i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.9494 | − | 25.8931i | −0.0572773 | − | 0.0992072i | ||||
\(262\) | −24.5366 | − | 14.1662i | −0.0936510 | − | 0.0540694i | ||||
\(263\) | 222.298 | − | 385.031i | 0.845238 | − | 1.46399i | −0.0401768 | − | 0.999193i | \(-0.512792\pi\) |
0.885415 | − | 0.464802i | \(-0.153875\pi\) | |||||||
\(264\) | 31.9776 | − | 18.4623i | 0.121127 | − | 0.0699329i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −106.069 | + | 213.723i | −0.398755 | + | 0.803471i | ||||
\(267\) | −24.0906 | −0.0902270 | ||||||||
\(268\) | 66.5822 | + | 115.324i | 0.248441 | + | 0.430312i | ||||
\(269\) | −144.956 | − | 83.6902i | −0.538869 | − | 0.311116i | 0.205752 | − | 0.978604i | \(-0.434036\pi\) |
−0.744620 | + | 0.667488i | \(0.767369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24099 | − | 1.29384i | 0.00826933 | − | 0.00477430i | −0.495860 | − | 0.868403i | \(-0.665147\pi\) |
0.504129 | + | 0.863628i | \(0.331814\pi\) | |||||||
\(272\) | − | 83.9498i | − | 0.308639i | ||||||
\(273\) | 232.311 | + | 115.294i | 0.850957 | + | 0.422322i | ||||
\(274\) | −121.864 | −0.444758 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 16.7403 | + | 9.66501i | 0.0606532 | + | 0.0350181i | ||||
\(277\) | 254.556 | − | 440.903i | 0.918973 | − | 1.59171i | 0.117996 | − | 0.993014i | \(-0.462353\pi\) |
0.800978 | − | 0.598694i | \(-0.204314\pi\) | |||||||
\(278\) | 284.756 | − | 164.404i | 1.02430 | − | 0.591381i | ||||
\(279\) | 19.7479i | 0.0707810i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 210.688 | 0.749779 | 0.374890 | − | 0.927069i | \(-0.377681\pi\) | ||||
0.374890 | + | 0.927069i | \(0.377681\pi\) | |||||||
\(282\) | 95.1005 | + | 164.719i | 0.337236 | + | 0.584110i | ||||
\(283\) | 34.1964 | + | 19.7433i | 0.120835 | + | 0.0697643i | 0.559199 | − | 0.829033i | \(-0.311109\pi\) |
−0.438364 | + | 0.898797i | \(0.644442\pi\) | |||||||
\(284\) | 68.1049 | − | 117.961i | 0.239806 | − | 0.415356i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 228.007i | − | 0.797229i | ||||||
\(287\) | −356.871 | + | 22.4852i | −1.24345 | + | 0.0783457i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 75.7363 | + | 131.179i | 0.262063 | + | 0.453907i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.19678 | + | 5.53698i | −0.0109855 | + | 0.0190274i | ||||
\(292\) | 151.826 | − | 87.6565i | 0.519951 | − | 0.300194i | ||||
\(293\) | − | 89.6023i | − | 0.305810i | −0.988241 | − | 0.152905i | \(-0.951137\pi\) | ||
0.988241 | − | 0.152905i | \(-0.0488628\pi\) | |||||||
\(294\) | −15.0649 | − | 119.076i | −0.0512412 | − | 0.405020i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 31.6735 | + | 54.8602i | 0.107005 | + | 0.185338i | ||||
\(297\) | 33.9174 | + | 19.5822i | 0.114200 | + | 0.0659334i | ||||
\(298\) | 155.511 | − | 269.354i | 0.521850 | − | 0.903871i | ||||
\(299\) | 103.370 | − | 59.6809i | 0.345720 | − | 0.199602i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3029 | + | 242.878i | 0.0508402 | + | 0.806903i | ||||
\(302\) | −368.999 | −1.22185 | ||||||||
\(303\) | 158.170 | + | 273.959i | 0.522013 | + | 0.904154i | ||||
\(304\) | −83.4914 | − | 48.2038i | −0.274643 | − | 0.158565i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 77.1128 | − | 44.5211i | 0.252003 | − | 0.145494i | ||||
\(307\) | − | 470.478i | − | 1.53250i | −0.642542 | − | 0.766251i | \(-0.722120\pi\) | ||
0.642542 | − | 0.766251i | \(-0.277880\pi\) | |||||||
\(308\) | −87.8852 | + | 58.4024i | −0.285341 | + | 0.189618i | ||||
\(309\) | 157.704 | 0.510370 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 217.631 | + | 125.649i | 0.699778 | + | 0.404017i | 0.807265 | − | 0.590189i | \(-0.200947\pi\) |
−0.107487 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(312\) | −52.3962 | + | 90.7528i | −0.167936 | + | 0.290874i | ||||
\(313\) | −336.417 | + | 194.231i | −1.07482 | + | 0.620545i | −0.929493 | − | 0.368839i | \(-0.879755\pi\) |
−0.145322 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(314\) | 161.490i | 0.514300i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 197.492 | 0.624974 | ||||||||
\(317\) | −74.6898 | − | 129.366i | −0.235614 | − | 0.408096i | 0.723837 | − | 0.689971i | \(-0.242377\pi\) |
−0.959451 | + | 0.281875i | \(0.909044\pi\) | |||||||
\(318\) | 105.637 | + | 60.9897i | 0.332193 | + | 0.191792i | ||||
\(319\) | 37.5588 | − | 65.0538i | 0.117739 | − | 0.203930i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 89.2636i | 0.278080i | ||||||||
\(322\) | −49.4815 | − | 24.5572i | −0.153669 | − | 0.0762645i | ||||
\(323\) | 505.837 | 1.56606 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −34.4475 | + | 59.6648i | −0.105667 | + | 0.183021i | ||||
\(327\) | 57.5420 | − | 33.2219i | 0.175970 | − | 0.101596i | ||||
\(328\) | − | 144.484i | − | 0.440499i | ||||||
\(329\) | −300.835 | − | 452.702i | −0.914391 | − | 1.37600i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 235.465 | + | 407.838i | 0.711375 | + | 1.23214i | 0.964341 | + | 0.264663i | \(0.0852607\pi\) |
−0.252966 | + | 0.967475i | \(0.581406\pi\) | |||||||
\(332\) | 46.6697 | + | 26.9448i | 0.140571 | + | 0.0811590i | ||||
\(333\) | −33.5948 | + | 58.1880i | −0.100885 | + | 0.174739i | ||||
\(334\) | 60.7628 | − | 35.0814i | 0.181925 | − | 0.105034i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 48.4014 | − | 3.04961i | 0.144052 | − | 0.00907622i | ||||
\(337\) | −532.478 | −1.58005 | −0.790027 | − | 0.613072i | \(-0.789934\pi\) | ||||
−0.790027 | + | 0.613072i | \(0.789934\pi\) | |||||||
\(338\) | 204.042 | + | 353.412i | 0.603676 | + | 1.04560i | ||||
\(339\) | 297.836 | + | 171.956i | 0.878573 | + | 0.507244i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42.9675 | + | 24.8073i | −0.126004 | + | 0.0727487i | ||||
\(342\) | − | 102.256i | − | 0.298993i | ||||||
\(343\) | 64.3643 | + | 336.907i | 0.187651 | + | 0.982236i | ||||
\(344\) | −98.3321 | −0.285849 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 288.232 | + | 166.411i | 0.833042 | + | 0.480957i | ||||
\(347\) | −224.812 | + | 389.385i | −0.647872 | + | 1.12215i | 0.335758 | + | 0.941948i | \(0.391008\pi\) |
−0.983630 | + | 0.180199i | \(0.942326\pi\) | |||||||
\(348\) | −29.8988 | + | 17.2621i | −0.0859160 | + | 0.0496036i | ||||
\(349\) | − | 330.676i | − | 0.947495i | −0.880661 | − | 0.473747i | \(-0.842901\pi\) | ||
0.880661 | − | 0.473747i | \(-0.157099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −111.149 | −0.316664 | ||||||||
\(352\) | −21.3184 | − | 36.9246i | −0.0605637 | − | 0.104899i | ||||
\(353\) | 235.014 | + | 135.686i | 0.665763 | + | 0.384379i | 0.794469 | − | 0.607304i | \(-0.207749\pi\) |
−0.128706 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(354\) | −103.147 | + | 178.657i | −0.291377 | + | 0.504680i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 27.8174i | 0.0781389i | ||||||||
\(357\) | −211.932 | + | 140.835i | −0.593646 | + | 0.394496i | ||||
\(358\) | −62.5221 | −0.174643 | ||||||||
\(359\) | 3.79200 | + | 6.56794i | 0.0105627 | + | 0.0182951i | 0.871258 | − | 0.490825i | \(-0.163304\pi\) |
−0.860696 | + | 0.509120i | \(0.829971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 109.950 | − | 190.440i | 0.304572 | − | 0.527534i | ||||
\(362\) | 143.355 | − | 82.7661i | 0.396009 | − | 0.228636i | ||||
\(363\) | − | 111.181i | − | 0.306285i | ||||||
\(364\) | 133.130 | − | 268.250i | 0.365741 | − | 0.736951i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −102.446 | − | 177.442i | −0.279908 | − | 0.484814i | ||||
\(367\) | 460.216 | + | 265.706i | 1.25400 | + | 0.723995i | 0.971901 | − | 0.235392i | \(-0.0756373\pi\) |
0.282095 | + | 0.959386i | \(0.408971\pi\) | |||||||
\(368\) | 11.1602 | − | 19.3300i | 0.0303266 | − | 0.0525272i | ||||
\(369\) | 132.717 | − | 76.6240i | 0.359666 | − | 0.207653i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −312.246 | − | 154.965i | −0.841634 | − | 0.417695i | ||||
\(372\) | 22.8029 | 0.0612981 | ||||||||
\(373\) | −287.484 | − | 497.937i | −0.770734 | − | 1.33495i | −0.937161 | − | 0.348897i | \(-0.886556\pi\) |
0.166427 | − | 0.986054i | \(-0.446777\pi\) | |||||||
\(374\) | 193.738 | + | 111.855i | 0.518016 | + | 0.299077i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 190.201 | − | 109.813i | 0.505854 | − | 0.292055i | ||||
\(377\) | 213.185i | 0.565476i | ||||||||
\(378\) | 28.4700 | + | 42.8423i | 0.0753174 | + | 0.113339i | ||||
\(379\) | 627.464 | 1.65558 | 0.827789 | − | 0.561040i | \(-0.189598\pi\) | ||||
0.827789 | + | 0.561040i | \(0.189598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 111.170 | + | 64.1839i | 0.291784 | + | 0.168462i | ||||
\(382\) | −165.684 | + | 286.973i | −0.433727 | + | 0.751238i | ||||
\(383\) | 57.6870 | − | 33.3056i | 0.150619 | − | 0.0869597i | −0.422797 | − | 0.906225i | \(-0.638952\pi\) |
0.573415 | + | 0.819265i | \(0.305618\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.6691 | −0.0716817 | ||||||||
\(387\) | −52.1485 | − | 90.3238i | −0.134751 | − | 0.233395i | ||||
\(388\) | 6.39356 | + | 3.69132i | 0.0164782 | + | 0.00951372i | ||||
\(389\) | −274.525 | + | 475.491i | −0.705719 | + | 1.22234i | 0.260713 | + | 0.965416i | \(0.416043\pi\) |
−0.966431 | + | 0.256925i | \(0.917291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 117.112i | 0.299519i | ||||||||
\(392\) | −137.497 | + | 17.3955i | −0.350757 | + | 0.0443762i | ||||
\(393\) | −34.7000 | −0.0882950 | ||||||||
\(394\) | 126.885 | + | 219.772i | 0.322044 | + | 0.557796i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 22.6116 | − | 39.1644i | 0.0571000 | − | 0.0989001i | ||||
\(397\) | −449.091 | + | 259.283i | −1.13121 | + | 0.653106i | −0.944240 | − | 0.329259i | \(-0.893201\pi\) |
−0.186973 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(398\) | 361.920i | 0.909347i | ||||||||
\(399\) | 18.3753 | + | 291.642i | 0.0460535 | + | 0.730931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 238.149 | + | 412.486i | 0.593888 | + | 1.02864i | 0.993703 | + | 0.112048i | \(0.0357411\pi\) |
−0.399815 | + | 0.916596i | \(0.630926\pi\) | |||||||
\(402\) | 141.242 | + | 81.5462i | 0.351349 | + | 0.202851i | ||||
\(403\) | 70.4033 | − | 121.942i | 0.174698 | − | 0.302586i | ||||
\(404\) | 316.340 | − | 182.639i | 0.783020 | − | 0.452077i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 82.1717 | − | 54.6056i | 0.202393 | − | 0.134497i | ||||
\(407\) | −168.807 | −0.414760 | ||||||||
\(408\) | −51.4085 | − | 89.0422i | −0.126001 | − | 0.218241i | ||||
\(409\) | −93.2552 | − | 53.8409i | −0.228008 | − | 0.131640i | 0.381645 | − | 0.924309i | \(-0.375358\pi\) |
−0.609653 | + | 0.792669i | \(0.708691\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −129.256 | + | 74.6259i | −0.314491 | + | 0.181572i | ||||
\(412\) | − | 182.101i | − | 0.441993i | ||||||
\(413\) | 262.080 | − | 528.079i | 0.634577 | − | 1.27864i | ||||
\(414\) | 23.6743 | 0.0571844 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 104.792 | + | 60.5019i | 0.251905 | + | 0.145437i | ||||
\(417\) | 201.353 | − | 348.753i | 0.482861 | − | 0.836339i | ||||
\(418\) | 222.488 | − | 128.454i | 0.532268 | − | 0.307305i | ||||
\(419\) | 323.811i | 0.772818i | 0.922328 | + | 0.386409i | \(0.126285\pi\) | ||||
−0.922328 | + | 0.386409i | \(0.873715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −238.957 | −0.567595 | −0.283797 | − | 0.958884i | \(-0.591594\pi\) | ||||
−0.283797 | + | 0.958884i | \(0.591594\pi\) | |||||||
\(422\) | −139.223 | − | 241.141i | −0.329912 | − | 0.571424i | ||||
\(423\) | 201.739 | + | 116.474i | 0.476924 | + | 0.275352i | ||||
\(424\) | 70.4249 | − | 121.979i | 0.166096 | − | 0.287687i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 166.822i | − | 0.391601i | ||||||
\(427\) | 324.071 | + | 487.670i | 0.758950 | + | 1.14208i | ||||
\(428\) | 103.073 | 0.240824 | ||||||||
\(429\) | −139.625 | − | 241.838i | −0.325467 | − | 0.563726i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 95.8960 | − | 166.097i | 0.222497 | − | 0.385375i | −0.733069 | − | 0.680154i | \(-0.761913\pi\) |
0.955565 | + | 0.294779i | \(0.0952461\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 122.083i | − | 0.281946i | −0.990013 | − | 0.140973i | \(-0.954977\pi\) | ||
0.990013 | − | 0.140973i | \(-0.0450231\pi\) | |||||||
\(434\) | −65.0358 | + | 4.09768i | −0.149852 | + | 0.00944166i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.3614 | − | 66.4438i | −0.0879848 | − | 0.152394i | ||||
\(437\) | 116.472 | + | 67.2454i | 0.266527 | + | 0.153880i | ||||
\(438\) | 107.357 | − | 185.948i | 0.245107 | − | 0.424538i | ||||
\(439\) | −217.656 | + | 125.664i | −0.495800 | + | 0.286250i | −0.726978 | − | 0.686661i | \(-0.759076\pi\) |
0.231177 | + | 0.972912i | \(0.425742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −88.8975 | − | 117.074i | −0.201582 | − | 0.265473i | ||||
\(442\) | −634.890 | −1.43640 | ||||||||
\(443\) | 54.8946 | + | 95.0802i | 0.123916 | + | 0.214628i | 0.921309 | − | 0.388832i | \(-0.127121\pi\) |
−0.797393 | + | 0.603460i | \(0.793788\pi\) | |||||||
\(444\) | 67.1897 | + | 38.7920i | 0.151328 | + | 0.0873693i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −527.883 | + | 304.773i | −1.18359 | + | 0.683349i | ||||
\(447\) | − | 380.924i | − | 0.852178i | ||||||
\(448\) | −3.52139 | − | 55.8892i | −0.00786024 | − | 0.124753i | ||||
\(449\) | 806.490 | 1.79619 | 0.898095 | − | 0.439801i | \(-0.144951\pi\) | ||||
0.898095 | + | 0.439801i | \(0.144951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 333.437 | + | 192.510i | 0.739329 | + | 0.426852i | ||||
\(452\) | 198.558 | − | 343.912i | 0.439287 | − | 0.760867i | ||||
\(453\) | −391.383 | + | 225.965i | −0.863980 | + | 0.498819i | ||||
\(454\) | − | 247.623i | − | 0.545425i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −118.075 | −0.258936 | ||||||||
\(457\) | −386.226 | − | 668.964i | −0.845135 | − | 1.46382i | −0.885504 | − | 0.464631i | \(-0.846187\pi\) |
0.0403698 | − | 0.999185i | \(-0.487146\pi\) | |||||||
\(458\) | −41.1137 | − | 23.7370i | −0.0897678 | − | 0.0518275i | ||||
\(459\) | 54.5270 | − | 94.4435i | 0.118795 | − | 0.205759i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 793.611i | − | 1.72150i | −0.509029 | − | 0.860749i | \(-0.669995\pi\) | ||
0.509029 | − | 0.860749i | \(-0.330005\pi\) | |||||||
\(462\) | −57.4523 | + | 115.764i | −0.124356 | + | 0.250570i | ||||
\(463\) | 274.227 | 0.592284 | 0.296142 | − | 0.955144i | \(-0.404300\pi\) | ||||
0.296142 | + | 0.955144i | \(0.404300\pi\) | |||||||
\(464\) | 19.9325 | + | 34.5241i | 0.0429580 | + | 0.0744054i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 109.540 | − | 189.730i | 0.235065 | − | 0.407145i | ||||
\(467\) | −344.357 | + | 198.815i | −0.737381 | + | 0.425727i | −0.821116 | − | 0.570761i | \(-0.806648\pi\) |
0.0837354 | + | 0.996488i | \(0.473315\pi\) | |||||||
\(468\) | 128.344i | 0.274239i | ||||||||
\(469\) | −417.488 | − | 207.195i | −0.890166 | − | 0.441781i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 98.8921 | + | 171.286i | 0.209962 | + | 0.363665i | ||||
\(472\) | 206.295 | + | 119.104i | 0.437065 | + | 0.252340i | ||||
\(473\) | 131.018 | − | 226.930i | 0.276993 | − | 0.479766i | ||||
\(474\) | 209.472 | − | 120.939i | 0.441923 | − | 0.255145i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 162.622 | + | 244.717i | 0.341643 | + | 0.514112i | ||||
\(477\) | 149.394 | 0.313194 | ||||||||
\(478\) | −223.864 | − | 387.743i | −0.468334 | − | 0.811179i | ||||
\(479\) | −165.573 | − | 95.5938i | −0.345665 | − | 0.199570i | 0.317110 | − | 0.948389i | \(-0.397288\pi\) |
−0.662774 | + | 0.748819i | \(0.730621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 414.893 | − | 239.538i | 0.862563 | − | 0.498001i | ||||
\(482\) | − | 330.223i | − | 0.685110i | ||||||
\(483\) | −67.5212 | + | 4.25428i | −0.139795 | + | 0.00880803i | ||||
\(484\) | −128.381 | −0.265250 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −95.0092 | + | 164.561i | −0.195091 | + | 0.337907i | −0.946930 | − | 0.321439i | \(-0.895833\pi\) |
0.751840 | + | 0.659346i | \(0.229167\pi\) | |||||||
\(488\) | −204.892 | + | 118.295i | −0.419862 | + | 0.242407i | ||||
\(489\) | 84.3788i | 0.172554i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −211.384 | −0.430517 | −0.215258 | − | 0.976557i | \(-0.569059\pi\) | ||||
−0.215258 | + | 0.976557i | \(0.569059\pi\) | |||||||
\(492\) | −88.4777 | − | 153.248i | −0.179833 | − | 0.311480i | ||||
\(493\) | −181.143 | − | 104.583i | −0.367430 | − | 0.212136i | ||||
\(494\) | −364.552 | + | 631.423i | −0.737960 | + | 1.27818i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 26.3305i | − | 0.0530857i | ||||||
\(497\) | 29.9779 | + | 475.791i | 0.0603178 | + | 0.957325i | ||||
\(498\) | 66.0010 | 0.132532 | ||||||||
\(499\) | 126.864 | + | 219.734i | 0.254236 | + | 0.440349i | 0.964688 | − | 0.263396i | \(-0.0848427\pi\) |
−0.710452 | + | 0.703746i | \(0.751509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.9658 | − | 74.4190i | 0.0857601 | − | 0.148541i | ||||
\(502\) | −69.4282 | + | 40.0844i | −0.138303 | + | 0.0798494i | ||||
\(503\) | 217.815i | 0.433033i | 0.976279 | + | 0.216516i | \(0.0694695\pi\) | ||||
−0.976279 | + | 0.216516i | \(0.930531\pi\) | |||||||
\(504\) | 49.4700 | − | 32.8743i | 0.0981547 | − | 0.0652268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 29.7397 | + | 51.5107i | 0.0587741 | + | 0.101800i | ||||
\(507\) | 432.839 | + | 249.900i | 0.853727 | + | 0.492899i | ||||
\(508\) | 74.1132 | − | 128.368i | 0.145892 | − | 0.252693i | ||||
\(509\) | −24.6582 | + | 14.2364i | −0.0484444 | + | 0.0279694i | −0.524027 | − | 0.851702i | \(-0.675571\pi\) |
0.475582 | + | 0.879671i | \(0.342237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −272.776 | + | 549.630i | −0.533808 | + | 1.07560i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −62.6185 | − | 108.458i | −0.122063 | − | 0.211420i | ||||
\(514\) | −355.714 | − | 205.371i | −0.692050 | − | 0.399555i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −104.297 | + | 60.2159i | −0.202126 | + | 0.116697i | ||||
\(517\) | 585.258i | 1.13203i | ||||||||
\(518\) | −198.601 | − | 98.5640i | −0.383400 | − | 0.190278i | ||||
\(519\) | 407.622 | 0.785399 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 671.401 | + | 387.634i | 1.28868 | + | 0.744019i | 0.978418 | − | 0.206633i | \(-0.0662507\pi\) |
0.310260 | + | 0.950652i | \(0.399584\pi\) | |||||||
\(522\) | −21.1416 | + | 36.6184i | −0.0405012 | + | 0.0701501i | ||||
\(523\) | 88.7388 | − | 51.2334i | 0.169673 | − | 0.0979605i | −0.412759 | − | 0.910840i | \(-0.635435\pi\) |
0.582431 | + | 0.812880i | \(0.302101\pi\) | |||||||
\(524\) | 40.0681i | 0.0764657i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −628.752 | −1.19535 | ||||||||
\(527\) | 69.0763 | + | 119.644i | 0.131075 | + | 0.227028i | ||||
\(528\) | −45.2232 | − | 26.1096i | −0.0856500 | − | 0.0494501i | ||||
\(529\) | 248.931 | − | 431.162i | 0.470570 | − | 0.815050i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 252.659i | 0.475816i | ||||||||
\(532\) | 336.759 | − | 21.2180i | 0.633005 | − | 0.0398835i | ||||
\(533\) | −1092.69 | −2.05008 | ||||||||
\(534\) | 17.0346 | + | 29.5049i | 0.0319001 | + | 0.0552525i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 94.1614 | − | 163.092i | 0.175674 | − | 0.304277i | ||||
\(537\) | −66.3147 | + | 38.2868i | −0.123491 | + | 0.0712976i | ||||
\(538\) | 236.712i | 0.439984i | ||||||||
\(539\) | 143.056 | − | 340.491i | 0.265410 | − | 0.631709i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 408.868 | + | 708.180i | 0.755763 | + | 1.30902i | 0.944994 | + | 0.327088i | \(0.106067\pi\) |
−0.189231 | + | 0.981933i | \(0.560599\pi\) | |||||||
\(542\) | −3.16924 | − | 1.82976i | −0.00584730 | − | 0.00337594i | ||||
\(543\) | 101.367 | − | 175.573i | 0.186680 | − | 0.323340i | ||||
\(544\) | −102.817 | + | 59.3614i | −0.189002 | + | 0.109120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −23.0634 | − | 366.047i | −0.0422406 | − | 0.670416i | ||||
\(547\) | 204.209 | 0.373325 | 0.186662 | − | 0.982424i | \(-0.440233\pi\) | ||||
0.186662 | + | 0.982424i | \(0.440233\pi\) | |||||||
\(548\) | 86.1706 | + | 149.252i | 0.157246 | + | 0.272357i | ||||
\(549\) | −217.321 | − | 125.471i | −0.395849 | − | 0.228544i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −208.024 | + | 120.103i | −0.377539 | + | 0.217972i | ||||
\(552\) | − | 27.3368i | − | 0.0495231i | ||||||
\(553\) | −575.698 | + | 382.569i | −1.04105 | + | 0.691806i | ||||
\(554\) | −719.992 | −1.29962 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −402.706 | − | 232.502i | −0.724291 | − | 0.418169i | ||||
\(557\) | 268.036 | − | 464.253i | 0.481214 | − | 0.833487i | −0.518553 | − | 0.855045i | \(-0.673529\pi\) |
0.999768 | + | 0.0215578i | \(0.00686259\pi\) | |||||||
\(558\) | 24.1861 | − | 13.9639i | 0.0433443 | − | 0.0250249i | ||||
\(559\) | 743.660i | 1.33034i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 273.987 | 0.488391 | ||||||||
\(562\) | −148.979 | − | 258.039i | −0.265087 | − | 0.459144i | ||||
\(563\) | 857.029 | + | 494.806i | 1.52225 | + | 0.878874i | 0.999654 | + | 0.0262960i | \(0.00837123\pi\) |
0.522600 | + | 0.852578i | \(0.324962\pi\) | |||||||
\(564\) | 134.492 | − | 232.948i | 0.238462 | − | 0.413028i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 55.8424i | − | 0.0986616i | ||||||
\(567\) | 56.4324 | + | 28.0068i | 0.0995281 | + | 0.0493948i | ||||
\(568\) | −192.630 | −0.339137 | ||||||||
\(569\) | −248.330 | − | 430.120i | −0.436432 | − | 0.755922i | 0.560979 | − | 0.827830i | \(-0.310425\pi\) |
−0.997411 | + | 0.0719076i | \(0.977091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 71.0244 | − | 123.018i | 0.124386 | − | 0.215443i | −0.797107 | − | 0.603838i | \(-0.793637\pi\) |
0.921493 | + | 0.388395i | \(0.126971\pi\) | |||||||
\(572\) | −279.251 | + | 161.226i | −0.488201 | + | 0.281863i | ||||
\(573\) | 405.841i | 0.708274i | ||||||||
\(574\) | 279.884 | + | 421.176i | 0.487604 | + | 0.733757i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 328.551 | + | 189.689i | 0.569413 | + | 0.328751i | 0.756915 | − | 0.653514i | \(-0.226706\pi\) |
−0.187502 | + | 0.982264i | \(0.560039\pi\) | |||||||
\(578\) | 107.107 | − | 185.515i | 0.185307 | − | 0.320961i | ||||
\(579\) | −29.3476 | + | 16.9438i | −0.0506866 | + | 0.0292639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −188.240 | + | 11.8604i | −0.323993 | + | 0.0204137i | ||||
\(582\) | 9.04185 | 0.0155358 | ||||||||
\(583\) | 187.668 | + | 325.051i | 0.321901 | + | 0.557549i | ||||
\(584\) | −214.714 | − | 123.965i | −0.367661 | − | 0.212269i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −109.740 | + | 63.3584i | −0.187269 | + | 0.108120i | ||||
\(587\) | 234.204i | 0.398984i | 0.979899 | + | 0.199492i | \(0.0639292\pi\) | ||||
−0.979899 | + | 0.199492i | \(0.936071\pi\) | |||||||
\(588\) | −135.185 | + | 102.650i | −0.229906 | + | 0.174575i | ||||
\(589\) | 158.654 | 0.269361 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 269.164 | + | 155.402i | 0.455438 | + | 0.262948i | ||||
\(592\) | 44.7931 | − | 77.5840i | 0.0756641 | − | 0.131054i | ||||
\(593\) | 495.838 | − | 286.272i | 0.836152 | − | 0.482753i | −0.0198023 | − | 0.999804i | \(-0.506304\pi\) |
0.855954 | + | 0.517051i | \(0.172970\pi\) | |||||||
\(594\) | − | 55.3869i | − | 0.0932439i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −439.853 | −0.738008 | ||||||||
\(597\) | 221.630 | + | 383.874i | 0.371239 | + | 0.643006i | ||||
\(598\) | −146.188 | − | 84.4016i | −0.244461 | − | 0.141140i | ||||
\(599\) | −46.7105 | + | 80.9049i | −0.0779807 | + | 0.135067i | −0.902379 | − | 0.430944i | \(-0.858181\pi\) |
0.824398 | + | 0.566011i | \(0.191514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 167.140i | 0.278103i | 0.990285 | + | 0.139051i | \(0.0444053\pi\) | ||||
−0.990285 | + | 0.139051i | \(0.955595\pi\) | |||||||
\(602\) | 286.643 | − | 190.483i | 0.476151 | − | 0.316417i | ||||
\(603\) | 199.746 | 0.331255 | ||||||||
\(604\) | 260.922 | + | 451.930i | 0.431990 | + | 0.748229i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 223.686 | − | 387.436i | 0.369119 | − | 0.639333i | ||||
\(607\) | 796.002 | − | 459.572i | 1.31137 | − | 0.757120i | 0.329047 | − | 0.944314i | \(-0.393273\pi\) |
0.982323 | + | 0.187194i | \(0.0599392\pi\) | |||||||
\(608\) | 136.341i | 0.224245i | ||||||||
\(609\) | 53.7173 | − | 108.238i | 0.0882058 | − | 0.177730i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −830.484 | − | 1438.44i | −1.35922 | − | 2.35424i | ||||
\(612\) | −109.054 | − | 62.9623i | −0.178193 | − | 0.102880i | ||||
\(613\) | −389.718 | + | 675.011i | −0.635755 | + | 1.10116i | 0.350600 | + | 0.936525i | \(0.385978\pi\) |
−0.986355 | + | 0.164635i | \(0.947356\pi\) | |||||||
\(614\) | −576.215 | + | 332.678i | −0.938462 | + | 0.541821i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 133.672 | + | 66.3402i | 0.217000 | + | 0.107695i | ||||
\(617\) | −510.821 | −0.827911 | −0.413956 | − | 0.910297i | \(-0.635853\pi\) | ||||
−0.413956 | + | 0.910297i | \(0.635853\pi\) | |||||||
\(618\) | −111.514 | − | 193.148i | −0.180443 | − | 0.312536i | ||||
\(619\) | −808.792 | − | 466.956i | −1.30661 | − | 0.754372i | −0.325082 | − | 0.945686i | \(-0.605392\pi\) |
−0.981529 | + | 0.191314i | \(0.938725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.1104 | − | 14.4975i | 0.0404355 | − | 0.0233454i | ||||
\(622\) | − | 355.390i | − | 0.571367i | ||||||
\(623\) | −53.8862 | − | 81.0892i | −0.0864947 | − | 0.130159i | ||||
\(624\) | 148.199 | 0.237498 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 475.766 | + | 274.684i | 0.760009 | + | 0.438792i | ||||
\(627\) | 157.323 | − | 272.491i | 0.250914 | − | 0.434595i | ||||
\(628\) | 197.784 | − | 114.191i | 0.314943 | − | 0.181832i | ||||
\(629\) | 470.047i | 0.747292i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −614.861 | −0.974423 | −0.487212 | − | 0.873284i | \(-0.661986\pi\) | ||||
−0.487212 | + | 0.873284i | \(0.661986\pi\) | |||||||
\(632\) | −139.648 | − | 241.877i | −0.220962 | − | 0.382717i | ||||
\(633\) | −295.336 | − | 170.512i | −0.466566 | − | 0.269372i | ||||
\(634\) | −105.627 | + | 182.952i | −0.166605 | + | 0.288568i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 172.505i | − | 0.271234i | ||||||
\(637\) | 131.557 | + | 1039.85i | 0.206526 | + | 1.63242i | ||||
\(638\) | −106.232 | −0.166508 | ||||||||
\(639\) | −102.157 | − | 176.942i | −0.159871 | − | 0.276904i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 94.1724 | − | 163.111i | 0.146915 | − | 0.254464i | −0.783171 | − | 0.621807i | \(-0.786399\pi\) |
0.930086 | + | 0.367343i | \(0.119732\pi\) | |||||||
\(642\) | 109.325 | − | 63.1189i | 0.170288 | − | 0.0983161i | ||||
\(643\) | − | 23.8831i | − | 0.0371432i | −0.999828 | − | 0.0185716i | \(-0.994088\pi\) | ||
0.999828 | − | 0.0185716i | \(-0.00591187\pi\) | |||||||
\(644\) | 4.91242 | + | 77.9667i | 0.00762798 | + | 0.121066i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −357.681 | − | 619.521i | −0.553685 | − | 0.959011i | ||||
\(647\) | 939.928 | + | 542.667i | 1.45275 | + | 0.838744i | 0.998637 | − | 0.0522010i | \(-0.0166237\pi\) |
0.454111 | + | 0.890945i | \(0.349957\pi\) | |||||||
\(648\) | −12.7279 | + | 22.0454i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −549.735 | + | 317.390i | −0.847049 | + | 0.489044i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66.4715 | + | 44.1724i | −0.102107 | + | 0.0678531i | ||||
\(652\) | 97.4323 | 0.149436 | ||||||||
\(653\) | −317.852 | − | 550.536i | −0.486756 | − | 0.843087i | 0.513128 | − | 0.858312i | \(-0.328487\pi\) |
−0.999884 | + | 0.0152254i | \(0.995153\pi\) | |||||||
\(654\) | −81.3767 | − | 46.9829i | −0.124429 | − | 0.0718393i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −176.955 | + | 102.165i | −0.269749 | + | 0.155740i | ||||
\(657\) | − | 262.970i | − | 0.400258i | ||||||
\(658\) | −341.723 | + | 688.555i | −0.519336 | + | 1.04644i | ||||
\(659\) | −888.955 | −1.34895 | −0.674473 | − | 0.738300i | \(-0.735629\pi\) | ||||
−0.674473 | + | 0.738300i | \(0.735629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −656.362 | − | 378.951i | −0.992983 | − | 0.573299i | −0.0868187 | − | 0.996224i | \(-0.527670\pi\) |
−0.906165 | + | 0.422925i | \(0.861003\pi\) | |||||||
\(662\) | 332.998 | − | 576.770i | 0.503018 | − | 0.871253i | ||||
\(663\) | −673.402 | + | 388.789i | −1.01569 | + | 0.586409i | ||||
\(664\) | − | 76.2114i | − | 0.114776i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 95.0206 | 0.142674 | ||||||||
\(667\) | −27.8063 | − | 48.1620i | −0.0416886 | − | 0.0722068i | ||||
\(668\) | −85.9316 | − | 49.6127i | −0.128640 | − | 0.0742704i | ||||
\(669\) | −373.270 | + | 646.522i | −0.557952 | + | 0.966401i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 630.464i | − | 0.939589i | ||||||
\(672\) | −37.9600 | − | 57.1230i | −0.0564881 | − | 0.0850045i | ||||
\(673\) | −936.839 | −1.39203 | −0.696017 | − | 0.718026i | \(-0.745046\pi\) | ||||
−0.696017 | + | 0.718026i | \(0.745046\pi\) | |||||||
\(674\) | 376.519 | + | 652.150i | 0.558634 | + | 0.967582i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 288.560 | − | 499.800i | 0.426863 | − | 0.739349i | ||||
\(677\) | −214.062 | + | 123.589i | −0.316192 | + | 0.182554i | −0.649694 | − | 0.760196i | \(-0.725103\pi\) |
0.333502 | + | 0.942749i | \(0.391770\pi\) | |||||||
\(678\) | − | 486.365i | − | 0.717352i | ||||||
\(679\) | −25.7881 | + | 1.62482i | −0.0379795 | + | 0.00239296i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −151.637 | − | 262.644i | −0.222669 | − | 0.385673i | ||||
\(682\) | 60.7652 | + | 35.0828i | 0.0890986 | + | 0.0514411i | ||||
\(683\) | −350.887 | + | 607.755i | −0.513744 | + | 0.889831i | 0.486129 | + | 0.873887i | \(0.338409\pi\) |
−0.999873 | + | 0.0159438i | \(0.994925\pi\) | |||||||
\(684\) | −125.237 | + | 72.3057i | −0.183095 | + | 0.105710i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 367.112 | − | 317.059i | 0.535149 | − | 0.462185i | ||||
\(687\) | −58.1435 | −0.0846339 | ||||||||
\(688\) | 69.5313 | + | 120.432i | 0.101063 | + | 0.175046i | ||||
\(689\) | −922.498 | − | 532.604i | −1.33889 | − | 0.773011i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −530.850 | + | 306.486i | −0.768234 | + | 0.443540i | −0.832244 | − | 0.554409i | \(-0.812944\pi\) |
0.0640104 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(692\) | − | 470.682i | − | 0.680176i | ||||||
\(693\) | 9.95302 | + | 157.968i | 0.0143622 | + | 0.227948i | ||||
\(694\) | 635.863 | 0.916230 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 42.2832 | + | 24.4122i | 0.0607518 | + | 0.0350750i | ||||
\(697\) | 536.047 | − | 928.461i | 0.769078 | − | 1.33208i | ||||
\(698\) | −404.993 | + | 233.823i | −0.580220 | + | 0.334990i | ||||
\(699\) | − | 268.318i | − | 0.383860i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 161.307 | 0.230110 | 0.115055 | − | 0.993359i | \(-0.463296\pi\) | ||||
0.115055 | + | 0.993359i | \(0.463296\pi\) | |||||||
\(702\) | 78.5942 | + | 136.129i | 0.111958 | + | 0.193916i | ||||
\(703\) | 467.480 | + | 269.900i | 0.664979 | + | 0.383926i | ||||
\(704\) | −30.1488 | + | 52.2193i | −0.0428250 | + | 0.0741751i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 383.777i | − | 0.543593i | ||||||
\(707\) | −568.349 | + | 1145.20i | −0.803889 | + | 1.61980i | ||||
\(708\) | 291.745 | 0.412069 | ||||||||
\(709\) | −285.175 | − | 493.938i | −0.402222 | − | 0.696669i | 0.591772 | − | 0.806106i | \(-0.298429\pi\) |
−0.993994 | + | 0.109436i | \(0.965095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 148.119 | − | 256.549i | 0.208325 | − | 0.360829i | ||||
\(712\) | 34.0693 | − | 19.6699i | 0.0478501 | − | 0.0276263i | ||||
\(713\) | 36.7317i | 0.0515171i | ||||||||
\(714\) | 322.345 | + | 159.977i | 0.451464 | + | 0.224057i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 44.2098 | + | 76.5736i | 0.0617455 | + | 0.106946i | ||||
\(717\) | −474.887 | − | 274.176i | −0.662325 | − | 0.382393i | ||||
\(718\) | 5.36270 | − | 9.28847i | 0.00746894 | − | 0.0129366i | ||||
\(719\) | 431.817 | − | 249.310i | 0.600580 | − | 0.346745i | −0.168690 | − | 0.985669i | \(-0.553954\pi\) |
0.769270 | + | 0.638924i | \(0.220620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 352.755 | + | 530.834i | 0.489258 | + | 0.736246i | ||||
\(722\) | −310.987 | −0.430730 | ||||||||
\(723\) | −202.219 | − | 350.254i | −0.279695 | − | 0.484446i | ||||
\(724\) | −202.735 | − | 117.049i | −0.280020 | − | 0.161670i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −136.169 | + | 78.6171i | −0.187560 | + | 0.108288i | ||||
\(727\) | 1058.79i | 1.45638i | 0.685375 | + | 0.728190i | \(0.259638\pi\) | ||||
−0.685375 | + | 0.728190i | \(0.740362\pi\) | |||||||
\(728\) | −422.675 | + | 26.6313i | −0.580597 | + | 0.0365815i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −631.888 | − | 364.821i | −0.864416 | − | 0.499071i | ||||
\(732\) | −144.881 | + | 250.941i | −0.197925 | + | 0.342816i | ||||
\(733\) | −13.1068 | + | 7.56721i | −0.0178810 | + | 0.0103236i | −0.508914 | − | 0.860817i | \(-0.669953\pi\) |
0.491033 | + | 0.871141i | \(0.336620\pi\) | |||||||
\(734\) | − | 751.530i | − | 1.02388i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.5658 | −0.0428883 | ||||||||
\(737\) | 250.922 | + | 434.609i | 0.340463 | + | 0.589700i | ||||
\(738\) | −187.690 | − | 108.363i | −0.254322 | − | 0.146833i | ||||
\(739\) | 81.3819 | − | 140.958i | 0.110124 | − | 0.190741i | −0.805696 | − | 0.592329i | \(-0.798208\pi\) |
0.915820 | + | 0.401588i | \(0.131542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 892.967i | 1.20508i | ||||||||
\(742\) | 30.9991 | + | 491.998i | 0.0417778 | + | 0.663071i | ||||
\(743\) | −338.071 | −0.455009 | −0.227504 | − | 0.973777i | \(-0.573057\pi\) | ||||
−0.227504 | + | 0.973777i | \(0.573057\pi\) | |||||||
\(744\) | −16.1241 | − | 27.9277i | −0.0216722 | − | 0.0375373i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −406.564 | + | 704.189i | −0.544991 | + | 0.943953i | ||||
\(747\) | 70.0046 | − | 40.4172i | 0.0937143 | − | 0.0541060i | ||||
\(748\) | − | 316.373i | − | 0.422959i | ||||||
\(749\) | −300.462 | + | 199.666i | −0.401151 | + | 0.266577i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −239.087 | − | 414.111i | −0.318359 | − | 0.551413i | 0.661787 | − | 0.749692i | \(-0.269798\pi\) |
−0.980146 | + | 0.198279i | \(0.936465\pi\) | |||||||
\(752\) | −268.985 | − | 155.299i | −0.357693 | − | 0.206514i | ||||
\(753\) | −49.0932 | + | 85.0319i | −0.0651968 | + | 0.112924i | ||||
\(754\) | 261.097 | − | 150.744i | 0.346282 | − | 0.199926i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 32.3395 | − | 65.1625i | 0.0427771 | − | 0.0861938i | ||||
\(757\) | 397.788 | 0.525479 | 0.262739 | − | 0.964867i | \(-0.415374\pi\) | ||||
0.262739 | + | 0.964867i | \(0.415374\pi\) | |||||||
\(758\) | −443.684 | − | 768.483i | −0.585335 | − | 1.01383i | ||||
\(759\) | 63.0874 | + | 36.4236i | 0.0831192 | + | 0.0479889i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1264.02 | + | 729.785i | −1.66100 | + | 0.958981i | −0.688767 | + | 0.724983i | \(0.741848\pi\) |
−0.972237 | + | 0.233998i | \(0.924819\pi\) | |||||||
\(762\) | − | 181.540i | − | 0.238241i | ||||||
\(763\) | 240.536 | + | 119.376i | 0.315250 | + | 0.156456i | ||||
\(764\) | 468.625 | 0.613383 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −81.5817 | − | 47.1012i | −0.106503 | − | 0.0614898i | ||||
\(767\) | 900.755 | − | 1560.15i | 1.17439 | − | 2.03410i | ||||
\(768\) | 24.0000 | − | 13.8564i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 2.10093i | − | 0.00273203i | −0.999999 | − | 0.00136602i | \(-0.999565\pi\) | ||
0.999999 | − | 0.00136602i | \(-0.000434817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −503.055 | −0.652471 | ||||||||
\(772\) | 19.5650 | + | 33.8876i | 0.0253433 | + | 0.0438959i | ||||
\(773\) | −391.972 | − | 226.305i | −0.507079 | − | 0.292762i | 0.224553 | − | 0.974462i | \(-0.427908\pi\) |
−0.731632 | + | 0.681700i | \(0.761241\pi\) | |||||||
\(774\) | −73.7491 | + | 127.737i | −0.0952830 | + | 0.165035i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.4406i | − | 0.0134544i | ||||||
\(777\) | −271.007 | + | 17.0752i | −0.348786 | + | 0.0219758i | ||||
\(778\) | 776.473 | 0.998037 | ||||||||
\(779\) | −615.594 | − | 1066.24i | −0.790236 | − | 1.36873i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 256.660 | − | 444.548i | 0.328630 | − | 0.569204i | ||||
\(782\) | 143.432 | − | 82.8106i | 0.183417 | − | 0.105896i | ||||
\(783\) | 51.7862i | 0.0661381i | ||||||||
\(784\) | 118.530 | + | 156.098i | 0.151186 | + | 0.199105i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.5366 | + | 42.4986i | 0.0312170 | + | 0.0540694i | ||||
\(787\) | 112.676 | + | 65.0535i | 0.143171 | + | 0.0826601i | 0.569875 | − | 0.821732i | \(-0.306992\pi\) |
−0.426703 | + | 0.904392i | \(0.640325\pi\) | |||||||
\(788\) | 179.443 | − | 310.804i | 0.227719 | − | 0.394421i | ||||
\(789\) | −666.893 | + | 385.031i | −0.845238 | + | 0.487998i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 87.3997 | + | 1387.15i | 0.110493 | + | 1.75367i | ||||
\(792\) | −63.9553 | −0.0807516 | ||||||||
\(793\) | 894.632 | + | 1549.55i | 1.12816 | + | 1.95403i | ||||
\(794\) | 635.111 | + | 366.681i | 0.799888 | + | 0.461815i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 443.260 | − | 255.916i | 0.556859 | − | 0.321503i | ||||
\(797\) | 1170.92i | 1.46915i | 0.678525 | + | 0.734577i | \(0.262619\pi\) | ||||
−0.678525 | + | 0.734577i | \(0.737381\pi\) | |||||||
\(798\) | 344.193 | − | 228.727i | 0.431320 | − | 0.286625i | ||||
\(799\) | 1629.66 | 2.03962 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.1359 | + | 20.8631i | 0.0451135 | + | 0.0260463i | ||||
\(802\) | 336.794 | − | 583.344i | 0.419942 | − | 0.727361i | ||||
\(803\) | 572.170 | − | 330.342i | 0.712540 | − | 0.411385i | ||||
\(804\) | − | 230.647i | − | 0.286875i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −199.131 | −0.247060 | ||||||||
\(807\) | 144.956 | + | 251.071i | 0.179623 | + | 0.311116i | ||||
\(808\) | −447.372 | − | 258.291i | −0.553679 | − | 0.319667i | ||||
\(809\) | 102.442 | − | 177.435i | 0.126628 | − | 0.219327i | −0.795740 | − | 0.605639i | \(-0.792918\pi\) |
0.922368 | + | 0.386312i | \(0.126251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 541.011i | − | 0.667092i | −0.942734 | − | 0.333546i | \(-0.891755\pi\) | ||
0.942734 | − | 0.333546i | \(-0.108245\pi\) | |||||||
\(812\) | −124.982 | − | 62.0274i | −0.153919 | − | 0.0763884i | ||||
\(813\) | −4.48198 | −0.00551289 | ||||||||
\(814\) | 119.365 | + | 206.746i | 0.146640 | + | 0.253988i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −72.7026 | + | 125.925i | −0.0890964 | + | 0.154319i | ||||
\(817\) | −725.658 | + | 418.959i | −0.888198 | + | 0.512801i | ||||
\(818\) | 152.285i | 0.186168i | ||||||||
\(819\) | −248.620 | − | 374.128i | −0.303565 | − | 0.456811i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 212.913 | + | 368.777i | 0.259334 | + | 0.449180i | 0.966064 | − | 0.258304i | \(-0.0831636\pi\) |
−0.706730 | + | 0.707484i | \(0.749830\pi\) | |||||||
\(822\) | 182.795 | + | 105.537i | 0.222379 | + | 0.128391i | ||||
\(823\) | 385.497 | − | 667.700i | 0.468405 | − | 0.811301i | −0.530943 | − | 0.847407i | \(-0.678162\pi\) |
0.999348 | + | 0.0361067i | \(0.0114956\pi\) | |||||||
\(824\) | −223.028 | + | 128.765i | −0.270665 | + | 0.156268i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −832.081 | + | 52.4266i | −1.00736 | + | 0.0634704i | ||||
\(827\) | 448.579 | 0.542417 | 0.271209 | − | 0.962521i | \(-0.412577\pi\) | ||||
0.271209 | + | 0.962521i | \(0.412577\pi\) | |||||||
\(828\) | −16.7403 | − | 28.9950i | −0.0202177 | − | 0.0350181i | ||||
\(829\) | −737.022 | − | 425.520i | −0.889050 | − | 0.513293i | −0.0154183 | − | 0.999881i | \(-0.504908\pi\) |
−0.873632 | + | 0.486588i | \(0.838241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −763.667 | + | 440.903i | −0.918973 | + | 0.530569i | ||||
\(832\) | − | 171.125i | − | 0.205679i | ||||||
\(833\) | −948.103 | − | 398.341i | −1.13818 | − | 0.478201i | ||||
\(834\) | −569.512 | −0.682868 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −314.646 | − | 181.661i | −0.376370 | − | 0.217298i | ||||
\(837\) | 17.1022 | − | 29.6218i | 0.0204327 | − | 0.0353905i | ||||
\(838\) | 396.585 | − | 228.969i | 0.473252 | − | 0.273232i | ||||
\(839\) | − | 77.0829i | − | 0.0918747i | −0.998944 | − | 0.0459373i | \(-0.985373\pi\) | ||
0.998944 | − | 0.0459373i | \(-0.0146275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −741.674 | −0.881895 | ||||||||
\(842\) | 168.968 | + | 292.662i | 0.200675 | + | 0.347579i | ||||
\(843\) | −316.032 | − | 182.461i | −0.374890 | − | 0.216443i | ||||
\(844\) | −196.891 | + | 341.025i | −0.233283 | + | 0.404058i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 329.438i | − | 0.389407i | ||||||
\(847\) | 374.237 | − | 248.692i | 0.441839 | − | 0.293615i | ||||
\(848\) | −199.192 | −0.234896 | ||||||||
\(849\) | −34.1964 | − | 59.2299i | −0.0402784 | − | 0.0697643i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −62.4875 | + | 108.231i | −0.0734283 | + | 0.127182i | ||||
\(852\) | −204.315 | + | 117.961i | −0.239806 | + | 0.138452i | ||||
\(853\) | − | 176.785i | − | 0.207251i | −0.994616 | − | 0.103626i | \(-0.966956\pi\) | ||
0.994616 | − | 0.103626i | \(-0.0330443\pi\) | |||||||
\(854\) | 368.118 | − | 741.740i | 0.431052 | − | 0.868547i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −72.8835 | − | 126.238i | −0.0851442 | − | 0.147474i | ||||
\(857\) | 1080.14 | + | 623.618i | 1.26037 | + | 0.727676i | 0.973146 | − | 0.230187i | \(-0.0739339\pi\) |
0.287225 | + | 0.957863i | \(0.407267\pi\) | |||||||
\(858\) | −197.460 | + | 342.011i | −0.230140 | + | 0.398614i | ||||
\(859\) | 1319.99 | − | 762.098i | 1.53666 | − | 0.887192i | 0.537630 | − | 0.843181i | \(-0.319320\pi\) |
0.999031 | − | 0.0440111i | \(-0.0140137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 554.779 | + | 275.331i | 0.644343 | + | 0.319781i | ||||
\(862\) | −271.235 | −0.314658 | ||||||||
\(863\) | −718.043 | − | 1243.69i | −0.832032 | − | 1.44112i | −0.896424 | − | 0.443197i | \(-0.853844\pi\) |
0.0643926 | − | 0.997925i | \(-0.479489\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −149.520 | + | 86.3255i | −0.172656 | + | 0.0996830i | ||||
\(867\) | − | 262.358i | − | 0.302605i | ||||||
\(868\) | 51.0058 | + | 76.7547i | 0.0587625 | + | 0.0884271i | ||||
\(869\) | 744.268 | 0.856465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1233.42 | − | 712.118i | −1.41610 | − | 0.817586i | ||||
\(872\) | −54.2512 | + | 93.9658i | −0.0622146 | + | 0.107759i | ||||
\(873\) | 9.59033 | − | 5.53698i | 0.0109855 | − | 0.00634248i | ||||
\(874\) | − | 190.199i | − | 0.217619i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −303.651 | −0.346634 | ||||||||
\(877\) | −595.626 | − | 1031.65i | −0.679163 | − | 1.17634i | −0.975233 | − | 0.221179i | \(-0.929010\pi\) |
0.296070 | − | 0.955166i | \(-0.404324\pi\) | |||||||
\(878\) | 307.813 | + | 177.716i | 0.350584 | + | 0.202410i | ||||
\(879\) | −77.5978 | + | 134.403i | −0.0882797 | + | 0.152905i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 81.6610i | − | 0.0926912i | −0.998925 | − | 0.0463456i | \(-0.985242\pi\) | ||
0.998925 | − | 0.0463456i | \(-0.0147576\pi\) | |||||||
\(882\) | −80.5253 | + | 191.660i | −0.0912985 | + | 0.217302i | ||||
\(883\) | −506.404 | −0.573504 | −0.286752 | − | 0.958005i | \(-0.592576\pi\) | ||||
−0.286752 | + | 0.958005i | \(0.592576\pi\) | |||||||
\(884\) | 448.935 | + | 777.578i | 0.507845 | + | 0.879613i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 77.6327 | − | 134.464i | 0.0876215 | − | 0.151765i | ||||
\(887\) | 17.8700 | − | 10.3172i | 0.0201466 | − | 0.0116316i | −0.489893 | − | 0.871783i | \(-0.662964\pi\) |
0.510039 | + | 0.860151i | \(0.329631\pi\) | |||||||
\(888\) | − | 109.720i | − | 0.123559i | ||||||
\(889\) | 32.6227 | + | 517.766i | 0.0366959 | + | 0.582414i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.9174 | − | 58.7467i | −0.0380667 | − | 0.0659334i | ||||
\(892\) | 746.540 | + | 431.015i | 0.836928 | + | 0.483200i | ||||
\(893\) | 935.747 | − | 1620.76i | 1.04787 | − | 1.81496i | ||||
\(894\) | −466.534 | + | 269.354i | −0.521850 | + | 0.301290i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −65.9600 | + | 43.8324i | −0.0736161 | + | 0.0489201i | ||||
\(897\) | −206.741 | −0.230480 | ||||||||
\(898\) | −570.274 | − | 987.744i | −0.635049 | − | 1.09994i | ||||
\(899\) | −56.8149 | − | 32.8021i | −0.0631979 | − | 0.0364873i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 905.109 | − | 522.565i | 1.00456 | − | 0.579983i | ||||
\(902\) | − | 544.501i | − | 0.603659i | ||||||
\(903\) | 187.384 | − | 377.570i | 0.207513 | − | 0.418128i | ||||
\(904\) | −561.606 | −0.621245 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 553.499 | + | 319.563i | 0.610926 | + | 0.352718i | ||||
\(907\) | 128.404 | − | 222.402i | 0.141570 | − | 0.245206i | −0.786518 | − | 0.617567i | \(-0.788118\pi\) |
0.928088 | + | 0.372361i | \(0.121452\pi\) | |||||||
\(908\) | −303.275 | + | 175.096i | −0.334003 | + | 0.192837i | ||||
\(909\) | − | 547.917i | − | 0.602769i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1194.31 | 1.31098 | 0.655492 | − | 0.755202i | \(-0.272461\pi\) | ||||
0.655492 | + | 0.755202i | \(0.272461\pi\) | |||||||
\(912\) | 83.4914 | + | 144.611i | 0.0915476 | + | 0.158565i | ||||
\(913\) | 175.880 | + | 101.544i | 0.192639 | + | 0.111220i | ||||
\(914\) | −546.207 | + | 946.058i | −0.597600 | + | 1.03507i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 67.1383i | 0.0732951i | ||||||||
\(917\) | −77.6173 | − | 116.800i | −0.0846427 | − | 0.127372i | ||||
\(918\) | −154.226 | −0.168002 | ||||||||
\(919\) | 446.876 | + | 774.012i | 0.486263 | + | 0.842232i | 0.999875 | − | 0.0157900i | \(-0.00502633\pi\) |
−0.513612 | + | 0.858022i | \(0.671693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −407.446 | + | 705.717i | −0.442395 | + | 0.766251i | ||||
\(922\) | −971.971 | + | 561.168i | −1.05420 | + | 0.608642i | ||||
\(923\) | 1456.81i | 1.57834i | ||||||||
\(924\) | 182.406 | − | 11.4928i | 0.197409 | − | 0.0124381i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −193.908 | − | 335.859i | −0.209404 | − | 0.362698i | ||||
\(927\) | −236.556 | − | 136.576i | −0.255185 | − | 0.147331i | ||||
\(928\) | 28.1888 | − | 48.8245i | 0.0303759 | − | 0.0526126i | ||||
\(929\) | 295.237 | − | 170.455i | 0.317801 | − | 0.183482i | −0.332611 | − | 0.943064i | \(-0.607930\pi\) |
0.650412 | + | 0.759582i | \(0.274596\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −940.565 | + | 714.199i | −1.01027 | + | 0.767131i | ||||
\(932\) | −309.827 | −0.332432 | ||||||||
\(933\) | −217.631 | − | 376.948i | −0.233259 | − | 0.404017i | ||||
\(934\) | 486.994 | + | 281.166i | 0.521407 | + | 0.301034i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 157.188 | − | 90.7528i | 0.167936 | − | 0.0969581i | ||||
\(937\) | − | 217.347i | − | 0.231961i | −0.993251 | − | 0.115981i | \(-0.962999\pi\) | ||
0.993251 | − | 0.115981i | \(-0.0370010\pi\) | |||||||
\(938\) | 41.4473 | + | 657.825i | 0.0441869 | + | 0.701306i | ||||
\(939\) | 672.834 | 0.716544 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1226.68 | + | 708.226i | 1.30360 | + | 0.752631i | 0.981019 | − | 0.193912i | \(-0.0621177\pi\) |
0.322577 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(942\) | 139.855 | − | 242.235i | 0.148466 | − | 0.257150i | ||||
\(943\) | 246.857 | − | 142.523i | 0.261779 | − | 0.151138i | ||||
\(944\) | − | 336.878i | − | 0.356862i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −370.574 | −0.391728 | ||||||||
\(947\) | −692.365 | − | 1199.21i | −0.731114 | − | 1.26633i | −0.956408 | − | 0.292035i | \(-0.905667\pi\) |
0.225294 | − | 0.974291i | \(-0.427666\pi\) | |||||||
\(948\) | −296.238 | − | 171.033i | −0.312487 | − | 0.180415i | ||||
\(949\) | −937.515 | + | 1623.82i | −0.987897 | + | 1.71109i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 258.733i | 0.272064i | ||||||||
\(952\) | 184.725 | − | 372.212i | 0.194039 | − | 0.390979i | ||||
\(953\) | −1365.38 | −1.43272 | −0.716359 | − | 0.697732i | \(-0.754193\pi\) | ||||
−0.716359 | + | 0.697732i | \(0.754193\pi\) | |||||||
\(954\) | −105.637 | − | 182.969i | −0.110731 | − | 0.191792i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −316.591 | + | 548.352i | −0.331162 | + | 0.573590i | ||||
\(957\) | −112.676 | + | 65.0538i | −0.117739 | + | 0.0679768i | ||||
\(958\) | 270.380i | 0.282234i | ||||||||
\(959\) | −540.313 | − | 268.152i | −0.563413 | − | 0.279616i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −458.834 | − | 794.725i | −0.477455 | − | 0.826977i | ||||
\(962\) | −586.747 | − | 338.758i | −0.609924 | − | 0.352140i | ||||
\(963\) | 77.3046 | − | 133.895i | 0.0802748 | − | 0.139040i | ||||
\(964\) | −404.439 | + | 233.503i | −0.419542 | + | 0.242223i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 52.9551 | + | 79.6880i | 0.0548189 | + | 0.0824927i | ||||
\(967\) | 1718.05 | 1.77668 | 0.888341 | − | 0.459185i | \(-0.151858\pi\) | ||||
0.888341 | + | 0.459185i | \(0.151858\pi\) | |||||||
\(968\) | 90.7792 | + | 157.234i | 0.0937802 | + | 0.162432i | ||||
\(969\) | −758.755 | − | 438.068i | −0.783029 | − | 0.452082i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 387.463 | − | 223.702i | 0.399035 | − | 0.230383i | −0.287033 | − | 0.957921i | \(-0.592669\pi\) |
0.686068 | + | 0.727538i | \(0.259335\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1624.29 | − | 102.341i | 1.66937 | − | 0.105181i | ||||
\(974\) | 268.727 | 0.275900 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 289.762 | + | 167.294i | 0.296887 | + | 0.171408i | ||||
\(977\) | −910.447 | + | 1576.94i | −0.931880 | + | 1.61406i | −0.151775 | + | 0.988415i | \(0.548499\pi\) |
−0.780105 | + | 0.625648i | \(0.784835\pi\) | |||||||
\(978\) | 103.343 | − | 59.6648i | 0.105667 | − | 0.0610070i | ||||
\(979\) | 104.833i | 0.107082i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −115.084 | −0.117313 | ||||||||
\(982\) | 149.471 | + | 258.891i | 0.152211 | + | 0.263637i | ||||
\(983\) | 1438.65 | + | 830.607i | 1.46353 | + | 0.844972i | 0.999172 | − | 0.0406735i | \(-0.0129503\pi\) |
0.464362 | + | 0.885646i | \(0.346284\pi\) | |||||||
\(984\) | −125.126 | + | 216.725i | −0.127161 | + | 0.220249i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 295.806i | 0.300006i | ||||||||
\(987\) | 59.2000 | + | 939.584i | 0.0599797 | + | 0.951960i | ||||
\(988\) | 1031.11 | 1.04363 | ||||||||
\(989\) | −96.9978 | − | 168.005i | −0.0980767 | − | 0.169874i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −275.795 | + | 477.690i | −0.278299 | + | 0.482029i | −0.970962 | − | 0.239233i | \(-0.923104\pi\) |
0.692663 | + | 0.721261i | \(0.256437\pi\) | |||||||
\(992\) | −32.2482 | + | 18.6185i | −0.0325082 | + | 0.0187686i | ||||
\(993\) | − | 815.676i | − | 0.821426i | ||||||
\(994\) | 561.525 | − | 373.150i | 0.564914 | − | 0.375403i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −46.6697 | − | 80.8344i | −0.0468572 | − | 0.0811590i | ||||
\(997\) | 1562.86 | + | 902.319i | 1.56757 | + | 0.905034i | 0.996452 | + | 0.0841629i | \(0.0268216\pi\) |
0.571113 | + | 0.820871i | \(0.306512\pi\) | |||||||
\(998\) | 179.412 | − | 310.751i | 0.179772 | − | 0.311374i | ||||
\(999\) | 100.785 | − | 58.1880i | 0.100885 | − | 0.0582462i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.p.c.451.1 | ✓ | 8 | |
5.2 | odd | 4 | 1050.3.q.b.199.6 | 16 | |||
5.3 | odd | 4 | 1050.3.q.b.199.3 | 16 | |||
5.4 | even | 2 | 1050.3.p.d.451.4 | yes | 8 | ||
7.5 | odd | 6 | inner | 1050.3.p.c.901.1 | yes | 8 | |
35.12 | even | 12 | 1050.3.q.b.649.3 | 16 | |||
35.19 | odd | 6 | 1050.3.p.d.901.4 | yes | 8 | ||
35.33 | even | 12 | 1050.3.q.b.649.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1050.3.p.c.901.1 | yes | 8 | 7.5 | odd | 6 | inner | |
1050.3.p.d.451.4 | yes | 8 | 5.4 | even | 2 | ||
1050.3.p.d.901.4 | yes | 8 | 35.19 | odd | 6 | ||
1050.3.q.b.199.3 | 16 | 5.3 | odd | 4 | |||
1050.3.q.b.199.6 | 16 | 5.2 | odd | 4 | |||
1050.3.q.b.649.3 | 16 | 35.12 | even | 12 | |||
1050.3.q.b.649.6 | 16 | 35.33 | even | 12 |